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Title: Graphical models for stationary time series Authors:  Sumanta Basu - Cornell University (United States) [presenting]
Abstract: A spectral precision matrix, the inverse of a spectral density matrix, is an object of central interest in frequency-domain multivariate time series analysis. The estimation of the spectral precision matrix is a key step in calculating partial coherency and graphical model selection of stationary time series. When the dimension of a multivariate time series is moderate to large, traditional estimators of spectral density matrices such as averaged periodograms tend to be severely ill-conditioned, and one needs to resort to suitable regularization strategies. We propose a complex graphical lasso (cglasso), an l1-penalized estimator of spectral precision matrix based on local Whittle likelihood maximization. We develop fast pathwise coordinate descent algorithms to implement cglasso for large dimensional time series. We also present a complete non-asymptotic theory of our proposed estimator which shows that consistent estimation is possible in a high-dimensional regime as long as the underlying spectral precision matrix is suitably sparse. We illustrate the advantage of cglasso over competing alternatives using extensive numerical experiments on simulated data sets.